Question: Solve for $x$ and $y$ using substitution. ${-x+3y = 3}$ ${x = 5y+1}$
Answer: Since $x$ has already been solved for, substitute $5y+1$ for $x$ in the first equation. ${-}{(5y+1)}{+ 3y = 3}$ Simplify and solve for $y$ $-5y-1 + 3y = 3$ $-2y-1 = 3$ $-2y-1{+1} = 3{+1}$ $-2y = 4$ $\dfrac{-2y}{{-2}} = \dfrac{4}{{-2}}$ ${y = -2}$ Now that you know ${y = -2}$ , plug it back into $\thinspace {x = 5y+1}\thinspace$ to find $x$ ${x = 5}{(-2)}{ + 1}$ $x = -10 + 1$ ${x = -9}$ You can also plug ${y = -2}$ into $\thinspace {-x+3y = 3}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(-2)}{= 3}$ ${x = -9}$